"We sure are pleased," he said. "Basically our family has gotten so much support from each other and friends. ... The local church took us under their wing and my co-workers have been so kind to all of us."

Addison has a 4-year-old biological brother who has been in counseling since his mother died.

"He still thinks about his mother and misses her," said Cox, 37. "But talking to a 4-year-old kid about anything can be difficult."

Addison also has two teenage stepbrothers. Cox's mother, who is from Texas, has been living with the family to help out for the last nearly two years.

The cancer has affected the child's brain, shoulder, lungs, kidney, liver, leg, and even the back of her tongue. She has had chemotherapy, radiation and brain surgeries at Phoenix Children's Hospital, which is hosting a telethon to benefit the family.

The toddler has been on chemotherapy for 20 months and has undergone radiation. A month ago she had two brain surgeries four days apart.

A fundraiser by the police department where Briana Cox worked has helped the family deal with their financial needs. "Most has been covered by medical insurance, but it's the cost of day-to-day life that really hammers us," said Cox.

So far, Addison has progressed well, understanding speech and saying a few words, like any child her age, according to her father.

"That gives you a lot to look forward to and know she's still doing this well, it just kind of keeps you going," said James.

"One hundred percent of the proceeds raised will have a direct impact on care, along with critical programs services provided to patients and families," said hospital spokeswoman Stacy Dillier.

Addison's mother had a malignant skin melanoma removed in 2006 and was assured by her doctors that the cancer had not spread and all her margins were clear.

Briana Cox went on to have a son David, now 4, and again became pregnant with her daughter Addison.

But just two months after the baby was born, in June 2011, Cox had a seizure and collapsed during a run. Scans revealed her brain and other parts of her body were riddled with advanced cancer.

And when four dark bumps appeared on baby Addison's forehead in September, she too was diagnosed with the same stage-four melanoma.

Cox died in February of 2012, but her last wish was to tell her family's private, but painful story to help others better understand the dangers of the disease.

Her husband was in the Azores, serving in the U.S. Air Force, when his wife was diagnosed. Today Cox is in emergency management.

"It was like running into a brick wall," he said in local press at the time. "It knocks the wind out of you. It was like being punched in the chest. And when Addison was [diagnosed], it was like being ejected from a car. You wonder, what's next?"

The phenomenon has only been recorded "a handful of times" in medical literature, according to Dr. Pooja Hingorani, a pediatric oncologist who treats Addison at Phoenix Children's Hospital.

"All cancer can happen in pregnancy," Hingorani told ABCNews.com last year. "But melanoma is the most common cancer to pass through the placenta from the mother."

About 30 percent of all mother-to-fetus cancers are melanoma, according to Hingorani, who said she has only seen four to five cases ever.

"When it is in the blood stream, it can go everywhere," she said.

Melanoma is a virulent form of skin cancer that begins in the cells that make the pigment melanin, but it can also begin in the eyes or intestines. According to the National Cancer Institute, about 76,000 new cases are diagnosed each year and 9,100 die of the disease.

Sun exposure is thought to be one of the causes of melanoma. Hingorani said cancer among women of childbearing age is on the rise, and those who are pregnant, should tell their doctors if they've had melanoma.

"After the birth, the placenta needs to be examined carefully," she said. "It's hard to say if we would have picked it up at birth, if Addison would have had a less extent of disease."

Meanwhile, Cox said he has been overjoyed with the medical care that Addison has received.

Cox said Addison's doctors hope to get her into clinical trials, if treatments start to fail.

"They got her in immediately when it was discovered, coordinated her care and are constantly looking forward to the next step."

"If Phoenix Children's had not been there," he said. "Addison would have already passed away."